The questions of mathematical modelling of indirect induction heating viscous oil in heaters and continuous optimization of the power distribution of internal heat sources on the criterion of maximum speed are analysed. It is similar to minimizing the length of the heater for the steady-state regimes of heating. The specificity of the heating of viscous fluids in indirect induction heating consists in the uneven distribution of liquid flow velocity in the cross section. proposed quasi-optimal algorithms for power distribution along the length of the heater in the form of a step function provide energy savings for heating when the technological demands of fidelity to the outlet temperature of the heater.